Differential protection is used for protecting generators, transformers, buses and power lines from the effects of internal faults, whereby the generator, transformer, bus or power line constitutes a protected zone of the differential protection. In the differential protection, the protected zone is delimited by current transformers connected to a protective relay, whereby a fault occurring inside the protected zone causes a protection operation provided by the protective relay, whereas no protection operation is caused by a fault occurring outside of the protected zone. The differential protection is thus an absolutely selective protection scheme since it only operates because of a fault occurring in a protected zone of its own.
In a differential protection scheme, currents on both sides of the protected zone are compared. The current comparison is carried out phase by phase such that the currents of the same phase on different sides of the protected zone are compared with each other. Under normal conditions, or in connection with a fault outside the protected zone, the currents on different sides of the protected zone are equal and there is no differential current flowing through the protective relay. If a fault develops inside the protected zone, the currents on different sides of the protected zone are no longer equal, which leads to a differential current flowing through the protective relay and causing the protective relay to operate.
Contrary to the ideal situation described above, in practice, there is usually some differential current originating, for example, from the magnetizing transformer current and current-dependent transformation errors of the current transformers as well as current transformer saturation. The magnetizing current is determined by the level of the system voltage and can therefore be viewed as constant, irrespective of load level. The transformation errors of the current transformers are, however, a function of the respective current level. The threshold value for the differential current in the protection operation of the protective relay is therefore not typically implemented as a constant differential current threshold value, but is formed as a function of a bias current, which can also be called a restraining current or a stabilizing current. The bias current represents the through-current of the zone being protected and it is widely used in differential protection to desensitize the protection in case of high currents flowing through the protected zone in order to avoid false operation of the protective relay due to differential currents that are not caused by the fault in the protected zone but by other reasons, some of which were explained above.
The general principle of the differential protection is further clarified with the following two examples relating to FIGS. 1(a) and 1(b). FIG. 1(a) discloses a schematic example of a two-terminal system including a first terminal T1 and a second terminal T2, where the first terminal T1 and the second terminal T2 form the protected zone. In a normal operating situation, there is a first terminal current IT1 flowing in to the protected zone and a second terminal current IT2 flowing out of the protected zone such that IT1=IT2, when the positive direction of the currents is determined to be towards the protected zone. Differential current Id(y) in a two-terminal system is determined asId(y)=IT1(y)+IT2(y)  (1)
One way to retrieve the bias current is to select the maximum of the currents flowing in and out of the protected zone, either phase-wise or by using one common bias for all phases. Another way is to take an average of the amplitudes of the currents flowing in and out of the protected zone.
A third way to retrieve the bias current for a two-terminal protected zone or a two-end protected zone, for example, for a two-winding transformer, is to take a phasor difference of currents flowing in and out of the protected zone per phase. Taking a phasor difference of currents flowing in and out of the protected zone is a good way to increase the sensitivity of the protection at internal faults while still maintaining the stability of the protection at through faults or other problematic situations. The stability of the protection means the capability of the protection to distinguish the differential current originating from a fault in the protected zone from differential currents originating from other reasons. When the positive direction of the current is defined to be towards the protected zone, the bias current per phase can be determined as follows:
                                          I                          b              ⁡                              (                y                )                                              =                                    1              2                        ⁢                                                                                              I                    _                                                        T                    ⁢                                                                                  ⁢                    1                    ⁢                                          (                      y                      )                                                                      -                                                      I                    _                                                        T                    ⁢                                                                                  ⁢                    2                    ⁢                                          (                      y                      )                                                                                                                        ,                            (        2        )            wherein Ib(y) is the bias current Ib in phase y, y=L1, L2, L3 for a three phase power system, IT1(y) is the phasor value of the current in phase y at the first terminal of the protected zone, for example, on a high voltage side of a power transformer, and IT2(y) is the phasor value of the current in phase y at the second terminal of the protected zone, for example, on a low voltage side of the power transformer. Further, as indicated above, the threshold value Id(y)—limit for the operation of the differential current protection is not typically implemented as a constant differential current threshold value but is formed as a function of a bias current, i.e.,Id(y)—limit=f(Ib(y))  (3)
In connection with an ideal through-fault or loading situation, the amplitude of the bias current corresponds to the amplitudes of the currents on opposite sides of the protected zone, i.e. Ib(y)=IT1(y)=IT2(y). Because the positive direction of the current is defined to be towards the protected zone as stated above, this means that in connection with the ideal through-fault or loading situation, the angle of the phasor IT1(y) is opposite to the angle of the phasor IT2(y), i.e., in connection with an ideal through-fault or loading situation IT1(y)=−IT2(y). In an internal fault which is fed from both directions, the bias current Ib decreases towards zero, causing maximum sensitivity to operating characteristics of the protection.
FIG. 1(b) discloses a schematic example of a three-terminal system including a first terminal T1, a second terminal T2 and a third terminal T3, where the first terminal T1, the second terminal T2 and the third terminal T3 form a protected zone. In a normal operating situation, there could be, for example, a first terminal current IT1 flowing in to the protected zone and a second terminal current IT2 and a third terminal current IT3 flowing out of the protected zone such that IT1=−(IT2+IT3), when the positive direction of the currents are determined to be towards the protected zone. Differential current Id(y) in a three-terminal system is determined asId(y)=IT1(y)+IT2(y)+IT3(y),  (4)and the bias current per phase is at the moment typically calculated by a sum of phasor current absolute values with an equation
                                          I                          b              ⁡                              (                y                )                                              =                                    1              X                        ⁢                          (                                                                                                            I                      _                                                              T                      ⁢                                                                                          ⁢                      1                      ⁢                                              (                        y                        )                                                                                                              +                                                                                              I                      _                                                              T                      ⁢                                                                                          ⁢                      2                      ⁢                                              (                        y                        )                                                                                                              +                                                                                              I                      _                                                              T                      ⁢                                                                                          ⁢                      3                      ⁢                                              (                        y                        )                                                                                                                          )                                      ,                            (        5        )            wherein IT3(y) is the phasor value of the current in phase y at the third terminal T3 of the protected zone and X is a scaling factor having a value of one or two, depending on the differential protection provider. In the case of equation (5) the bias effect never disappears in connection with an internal fault but it can be even reinforced in the case of multi-end infeed. The threshold value Id(y)—limit for the operation of the differential current protection is again formed as a function of a bias current according to equation (3).
In the determination of the bias current Ib as disclosed above, it should be noted that before the phase current of individual terminals or ends can be compared, they must first be matched with respect to the absolute values and phase angle values such that in fault-free operation under idealized conditions the corresponding phase currents of the individual terminals or ends are scaled so that they are equivalent in absolute value and phase angle value.